So what exactly is Donald Trump hiding in his unpublished tax returns?

Tax issues, famously, brought down Al Capone. Now Donald Trump has been called many things, but gangster is not among them. Even so, could tax issues – in his case the contents of his tax returns that he refuses to make public – prove the Achilles heel of his campaign for the White House?

Releasing tax records has become a rite of passage for presidential nominees. Every major party candidate since Richard Nixon has done so. It is now an essential part of the “getting to know you” process that shapes the public view of a candidate.

But Trump, as usual, isn’t playing by the established rules.

For the time being at least he is stonewalling, as he has done for years. The reasons have changed over time. Back in 2011 he said he’d release them when Barack Obama released his full birth certificate proving that, contrary to Trump’s suggestions, the 44th president had not been born in Kenya.

Then Trump promised he’d make his “beautiful” returns public in due course. Then he said he couldn’t because he’s under audit by the Internal Revenue Service. Which is nonsense: Nixon released his when he was being audited, and the IRS has recently confirmed that audits don’t prevent a person from releasing his returns should he or she so wish.

Now the property magnate insists “they’re none of anyone’s business,” and that in any case, “there’s nothing to learn from them.”

But if there’s nothing to hide, why not release them – certainly those up to 2008, on which audits apparently have been closed? No, says the Trump camp; all the annual returns are “connected”.

Trump’s foes in his party and beyond, however, think they know why he’s being so obdurate. Take Mitt Romney, the 2012 Republican nominee and an especially ferocious critic.

“There’s only one logical explanation: there’s a bombshell in them.” And Romney should know. Four years ago, he initially resisted similar pressure to release his returns, but in the end was forced to do so. They showed that Romney, with an estimated personal fortune of up to $250m, paid an effective income tax of only 14 per cent, and had investments in entities based in foreign tax havens such as the Cayman Islands.

All of which was fodder for the Obama campaign, as it portrayed Romney as a super-rich hedge fund operator hopelessly out of touch with ordinary Americans.

So what might the returns conceal, that Trump doesn’t want to come out? The possibilities are many.

Maybe he’s paying little or even no tax. The US tax code offers many loopholes to property developers. The last batch of Trump tax returns we do know about were made public in 1981, when New Jersey’s gambling regulators were vetting a Trump application to open a casino-hotel complex in the state. They cover the period 1975 to 1979. In the last two years Trump paid no tax whatsoever.

Up to a point, of course, that’s fine: Trump is a businessman who, like all businessmen (and the rest of us for that matter), want to reduce their tax bill as much as they can, within the limits of the law. But it wouldn’t sit well for a populist whose appeal partly rests on rants against corporate titans, hedge fund operators and the like, who in his words “make a fortune and pay no taxes,” and “get away with murder.”

They could also show Trump has used elaborate tax shelters, maybe offshore ones. They would also throw light on Trump’s tax-deductible charitable contributions. Is he as generous a donor as he claims.

More generally, they would provide some kind of gauge of his wealth – and could it be he’s nowhere near as rich as he brags (remember all those $10bn boasts)… and by extension maybe not quite the super-hotshot businessman he claims to be?

Whatever else, this issue – like the saga over Hillary Clinton’s State Department emails – won’t go away.

A Washington Post poll this week found that 60 per cent of independent voters (who Trump absolutely needs if he is to win in November) want him to release his returns. Almost all of them feel strongly about the matter. Almost half of Republicans believe Trump should do so – not to mention around 100 per cent, one presumes, of Democrats.

Clinton is already making hay with the Trump returns, and the pressure will only intensify as November approaches. Romney said he wouldn’t release his returns, but ultimately had no choice. It could be the same for Donald Trump.